Has anyone heard of an Alenax bike? Instead of pedaling a circular
motion, the pedals pump up and down vertically. Strangest riding
bike I've tried. A friend bought one at a garage sale.

The Alenax is a great example of an outsider inventing a solution to a
perceived problem, creating something that is useless for the intended
user. Much money was thrown into the design and manufacture of the
Alenax, and several years of bicycle-show attendance with many models.

As soon as you ride it, you'll realize why it doesn't work, even
though it has a continuously variable gear ratio. It isn't a CVT
(continuously variable transmission) because it relies on
reciprocating levers to pull the chains, essentially a rowing machine
on which the "oarlock" (fulcrum) is movable.

The main problem is that the invention is based on constant-velocity
lever pedals, instead of circular cranks on which the rotating foot
presents no inertial problems and on which the leg moves in sinusoidal
motion. The Alenax requires the foot to reach full speed from a stop
before it catches up to the load it is trying to propel, after which
it must stop suddenly from full speed at the bottom of the stroke.
The action can be simulated by propelling a conventional bicycle with
one foot locked into a pedal, rocking the pedal up and down through
a small arc about the forward position.

The early models had fully independent pedal levers that could be
pedaled singly or in parallel or only one if you wanted. This
made the return stroke difficult because the leg and crank had to be
pulled back to the top. What was worse is that in the event of a bump
in the road, the rider could not stand up, because both pedals would
go to the very bottom, fully extending the legs, preventing rising
from the saddle.

A later version employed a straddle cable over a pulley through which
one pedal raised the other, also enabling one to stand on both pedals
at half height as on a conventional bicycle.

Wheel changes were complicated by two chains, one on each side of the
rear wheel, each tensioned by a haulback spring. Each freewheel had
one sprocket but I can imagine a large and small one to give more
range with a smaller lever extension. The left side required a left-handed freewheel.

Summing it up, I think the inventor (and investors) did not realize
that converting reciprocating motion into circular motion is best done
by a rotary crank rather than a reciprocating lever, and above all,
they weren't bicyclists.